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26 April 2018, Volume 38 Issue 2 Previous Issue    Next Issue

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On Zeros and Periodicity of Entire Functions Wang Qiong, Hu Peichu Acta mathematica scientia,Series A. 2018, 38 (2):  209-214.  Abstract ( 207 )   RICH HTML PDF (257KB) ( 205 )   Save In this paper, we show that if f is a transcendental entire function such that (f2)(k) is periodic for a positive integer k, then f is also periodic. The result is related to a conjecture raised recently by Yang C C. References | Related Articles | Metrics

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Some Properties on the Classes of Analytic Functions Involving Hypergeometric Functions Peng Zhigang, Pan Wenjun, Xiong Songlin Acta mathematica scientia,Series A. 2018, 38 (2):  215-221.  Abstract ( 124 )   RICH HTML PDF (272KB) ( 116 )   Save Let A be the set of functions analytic in the unit disk D={z:|z|<1}. Let S*(α) denote the class of all starlike functions of order α. Let Rα denote the set of all functions prestarlike of order α (0 ≤ α ≤ 1). Also, let R(α, β) denote the set of all functions f∈A satisfying the conditions f(0)=f'(0)-1=0 and f*(z/(1-z)2(1-α))∈S*(β). In this article, the authors discuss the inclusion relations between R(α, β) and some convolution properties for Rα. References | Related Articles | Metrics

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Normality and Shared Function Concerning Differential Polynomials Deng Bingmao, Lei Chunlin, Fang Mingliang Acta mathematica scientia,Series A. 2018, 38 (2):  222-230.  Abstract ( 83 )   RICH HTML PDF (307KB) ( 92 )   Save Let m(≥ 0) be an integer, let h(z)(≢0) be a holomorphic function in a domain D with all zeros have multiplicity at most m, let P be a polynomial with either deg P ≥ 3 or deg P=2 and P having only one distinct zero, and let F be a family of meromorphic functions in a domain D, all of whose zeros and poles have multiplicity at least m+1. If, for each pair of functions f and g in F, P(f)f' and P(g)g' share h(z) in D, then F is normal in D. The result improved the results due to Lei and Fang[8], Zhang[16]. References | Related Articles | Metrics

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Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem Chang Shih-sen, Liu Zhenhai, Wen Ching-Feng, Tang Jinfang Acta mathematica scientia,Series A. 2018, 38 (2):  231-243.  Abstract ( 99 )   RICH HTML PDF (375KB) ( 97 )   Save The purpose of this paper is by using the shrinking projection method to introduce and study an iterative process to approximate a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup. As applications, we shall utilize the results to study the split optimization problem and the split variational inequality. References | Related Articles | Metrics

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The General Iterative Algorithms for Variational Inclusions and Fixed Point Problems Extended to Banach Spaces Without the Weakly Sequentially Continuous Duality Mapping Liu Ying Acta mathematica scientia,Series A. 2018, 38 (2):  244-263.  Abstract ( 99 )   RICH HTML PDF (429KB) ( 95 )   Save In this paper, we introduce an iterative scheme by the general iterative method for finding a common element of the set of solutions of a general system of nonlinear variational inclusions for two H-accretive mappings and the set of common fixed points of an infinite family of strictly pseudo-contractive mappings which solves some variational inequality in q-uniformly smooth Banach spaces without the weakly sequentially continuous duality mapping. Our results improve and extend the corresponding results announced by many others. References | Related Articles | Metrics

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The Well-Posedness of Degenerate Differential Equations with Finite Delay in Banach Spaces Cai Gang Acta mathematica scientia,Series A. 2018, 38 (2):  264-275.  Abstract ( 88 )   RICH HTML PDF (354KB) ( 111 )   Save In this paper, we study the well-posedness of the second order degenerate differential equation:(Mu')'(t)=Au(t) + Bu'(t) + Fut + f(t) (t ∈ T:=[0, 2π]) with periodic boundary conditions u(0)=u(2π),(Mu')(0)=(Mu')(2π), in Lebesgue-Bochner spaces Lp(T, X) and periodic Besov spaces Bp,qs(T, X). Using operator-valued Fourier multipliers theorems in vector-valued function spaces, we give necessary and sufficient conditions for the well-posedness of above equation. References | Related Articles | Metrics

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The Existence of Ground State to the Generalized Choquard-Pekar Equation with Superlinear Nonlinearities Yu Chun, Wan Youyan Acta mathematica scientia,Series A. 2018, 38 (2):  276-283.  Abstract ( 139 )   RICH HTML PDF (296KB) ( 109 )   Save In this paper the generalized Choquard-Pekar equation with superlinear nonlinearities was studied. By the concentration compactness principle, the minimal point on the Nehari manifold was achieved, then the existence of the ground state was obtained. References | Related Articles | Metrics

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The Existence of Global Weak Solutions to Thermohaline Circulation Equations Xing Chao, Ren Mengzhang, Luo Hong Acta mathematica scientia,Series A. 2018, 38 (2):  284-290.  Abstract ( 87 )   RICH HTML PDF (327KB) ( 99 )   Save In the article, the existence of global weak solutions to thermohaline circulation equations is proved by the theory of T-weakly continuous operator and the method of space sequence. Firstly, the space of test function and space of solution function are chosen according to thermohaline circulation equations. Then the equations can be rewritten as abstract operator equation. Furthermore, it is proved that the operator is T-weakly continuous and satisfies corresponding conditions. Thus the existence of global weak solutions to thermohaline circulation equations is obtained. References | Related Articles | Metrics

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Initial Value Problem for Nonlinear Fractional Differential Equations with Variable-order Derivative and a Parameter Zhang Shuqin, Hu Lei Acta mathematica scientia,Series A. 2018, 38 (2):  291-303.  Abstract ( 92 )   RICH HTML PDF (337KB) ( 88 )   Save In this work, we study the existence result of solution to an initial value problem for a differential equation involving with variable-order derivative. Our analysis relies on the Schauder fixed-point theorem and some analysis technique. References | Related Articles | Metrics

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A Blow-up Result for a Higher-Order Damped Hyperbolic System with Nonlinear Memory Terms Liu Dengming, Zeng Xianzhong, Mu Chunlai Acta mathematica scientia,Series A. 2018, 38 (2):  304-312.  Abstract ( 108 )   RICH HTML PDF (303KB) ( 89 )   Save In this paper, we deal with the Cauchy problem for a higher-order damped hyperbolic system with nonlinear memory terms. By the test function method, we obtain a blow-up result of the weak solution. References | Related Articles | Metrics

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Effect of Impulsive Perturbations on Oscillation of Nonlinear Delay Hyperbolic Distributed Parameter Systems Luo Liping, Luo Zhenguo, Deng Yihua Acta mathematica scientia,Series A. 2018, 38 (2):  313-321.  Abstract ( 136 )   RICH HTML PDF (332KB) ( 86 )   Save The oscillatory behavior for a class of nonlinear impulsive delay hyperbolic distributed parameter systems with higher order Laplace operator are investigated under third boundary value condition. By employing the technique of treating higher order Laplace operator and impulsive delay differential inequality, some new explicit sufficient criteria are established for the oscillation of such systems. The conclusions obtained fully show that the oscillation is caused by impulsive perturbation and delay effect. References | Related Articles | Metrics

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Instability of Plane Couette-Poiseuille Flow of Compressible Navier-Stokes Equation Wang Junli, Zhang Xingwei, Liu Jian Acta mathematica scientia,Series A. 2018, 38 (2):  322-333.  Abstract ( 103 )   RICH HTML PDF (326KB) ( 91 )   Save In this paper, we consider the instability of Plane Couette-Poiseuille flow of compressible Navier-Stokes equation. By the perturbation theory of linear operator, when the board speed is small, Mach number and Reynold number satisfy some condition, it turns out that plane Couette-Poiseuille flow of compressible Navier-Stokes equation is unstable. References | Related Articles | Metrics

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Comparison of Inequality Under Incomplete Information and Based on Schur-Convex Function Li Bang, Yu Jinghu Acta mathematica scientia,Series A. 2018, 38 (2):  334-349.  Abstract ( 94 )   RICH HTML PDF (458KB) ( 90 )   Save With the inequality increasingly prominent, the indicator to measure inequity is more and more important. Because of significant cost to collect data in inequality measure, it is very interesting to ask how to reduce the amount of data acquisition to compare the degree of inequality. The literatures on inequality keep silent on this problem. Since the indicator to measure inequity has a direct association with the Schur-convex function, based on the Schur-convex function and under the conditions of a few known variable values, this paper gives the sufficient conditions of the relationship of majorization between two variable vectors though determining the upper and lower bounds of majorization. Using this condition, we can compare the degree of inequality. And the application of Shannon entropy in inequality measure is given. References | Related Articles | Metrics

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The Existence of Invariant Measure for Markov Chains with Uniform Countable Additivity Zhang Ren, Zhang Shaoyi Acta mathematica scientia,Series A. 2018, 38 (2):  350-357.  Abstract ( 122 )   RICH HTML PDF (281KB) ( 80 )   Save In this paper, the main results are that state space admits the Harris decomposition for Markov chains when provided uniform countable additivity condition and drift condition (V1) are satisfied, furthermore, imply that there is an invariant measure. A relevant example is given. References | Related Articles | Metrics

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An Iterative Updating Method for Undamped Vibration Systems Using Acceleration and Displacement Feedback Zhang Qian, Yuan Yongxin Acta mathematica scientia,Series A. 2018, 38 (2):  358-371.  Abstract ( 110 )   RICH HTML PDF (376KB) ( 95 )   Save In this paper, an iterative method for simultaneously updating mass and stiffness matrices is presented. By the method, the required control gain matrices of acceleration and displacement feedback are determined, and thus the optimal approximation mass and stiffness matrices which satisfies the required eigenvalue equation are found under the Frobenius norm sense and the large number of unmeasured and unknown eigeninformation of the original model is preserved. Two numerical examples show that the proposed method is reliable and attractive. References | Related Articles | Metrics

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Research on the Effects of Different Sampling Algorithm on Sobol Sensitivity Analysis Liu Huan, Wu Qiongli, Cournède Paul-Henry Acta mathematica scientia,Series A. 2018, 38 (2):  372-384.  Abstract ( 171 )   RICH HTML PDF (458KB) ( 110 )   Save The Sobol method is one of the most important branch of sensitivity analysis. The produces of numerical solution of Sobol method mainly depend on the Monte Carlo method. While the generation of random numbers is the basis of Monte Carlo method. Pseudo random number generator is the most simple and basal method to generate random numbers. However, the uniformity of random numbers generated by pseudo random number generator is not very good. Thereby, the sample quality will be effected, and will affect the convergence and accuracy of sensitivity analysis indices calculated from the samples. In this paper, quasi random sampler and Latin hypercube sampler are used to substitute the pseudo sampler, then compare the samples get from them, and the accuracy and convergence of sensitivity analysis indices. Finally, the paper finds that quasi random sampling has obvious advantages compared with other two samplers. References | Related Articles | Metrics

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A New Absolutely Stable hp Discontinuous Galerkin Methodfor the Reaction-Diffusion Problem Ge Zhihao, Cao Jiwei Acta mathematica scientia,Series A. 2018, 38 (2):  385-394.  Abstract ( 109 )   RICH HTML PDF (708KB) ( 121 )   Save In this paper, a new absolutely stable hp discontinuous Galerkin method is proposed. And the error estimate of hp discontinuous Galerkin method is given, and the optimal convergent orders in L2-norm and H1-norm for the general stabilization parameters are proved. Finally, the numerical tests verify the theoretical results. References | Related Articles | Metrics

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Mixed Finite Volume Element Method and Numerical Simulation for Sine-Gordon Equation Fang Zhichao, Li Hong, Luo Zhendong, Liu Yang Acta mathematica scientia,Series A. 2018, 38 (2):  395-416.  Abstract ( 103 )   RICH HTML PDF (1957KB) ( 93 )   Save The mixed finite volume element method for the one-dimensional sine-Gordon equation with Dirichlet or Neumann boundary conditions is developed and studied. By introducing a transfer operator γh which maps the trial function space into the test function space and combining mixed finite element with finite volume method, the continuous-in-time, explicit-in-time and implicit-in-time mixed finite volume element schemes are constructed. Stability analysis for explicit-in-time scheme is given, and optimal error estimates for three schemes are obtained. Finally, numerical experiments are given to verify the theoretical results and the effectiveness of the proposed schemes. References | Related Articles | Metrics